IEEE Transactions on Information Theory最新文献_第2页

Optimal Codes in the Class of 2-Bit Delay Decodable Codes 2位延迟可解码码类的最优码

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-11-21 DOI: 10.1109/TIT.2024.3503717

Kengo Hashimoto;Ken-Ichi Iwata

{"title":"Optimal Codes in the Class of 2-Bit Delay Decodable Codes","authors":"Kengo Hashimoto;Ken-Ichi Iwata","doi":"10.1109/TIT.2024.3503717","DOIUrl":"https://doi.org/10.1109/TIT.2024.3503717","url":null,"abstract":"For an integer \u0000<inline-formula> <tex-math>$k geq 0$ </tex-math></inline-formula>\u0000, k-bit delay decodable code-tuples are source codes that use a finite number of code tables and allow a decoding delay of at most k bits. It is known that the class of k-bit delay decodable code-tuples can achieve a better average codeword length than Huffman codes for \u0000<inline-formula> <tex-math>$k geq 2$ </tex-math></inline-formula>\u0000. However, it is generally challenging to find an optimal k-bit delay decodable code-tuple (i.e., a k-bit delay decodable code-tuple achieving the optimal average codeword length among all k-bit delay decodable code-tuples) because the class of k-bit delay decodable code-tuples is a comprehensive and flexible class containing a variety of source code consisting of any finite number of code tables. AIFV (almost instantaneous fixed-to-variable length) codes are 2-bit delay decodable code-tuples consisting of two code tables satisfying certain constraints. This paper proves that the class of AIFV codes always contains an optimal 2-bit delay decodable code-tuple for any given source distribution. Thus, we can find an optimal 2-bit delay decodable code-tuple in the class of 2-bit delay decodable code-tuples by considering only the class of AIFV codes, which is a very restricted subclass compared to the whole class of 2-bit delay decodable code-tuples.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"797-832"},"PeriodicalIF":2.2,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Tradeoff Constructions for Quantum Locally Testable Codes 量子局部可测试码的权衡结构

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-11-20 DOI: 10.1109/TIT.2024.3503500

Adam Wills;Ting-Chun Lin;Min-Hsiu Hsieh

{"title":"Tradeoff Constructions for Quantum Locally Testable Codes","authors":"Adam Wills;Ting-Chun Lin;Min-Hsiu Hsieh","doi":"10.1109/TIT.2024.3503500","DOIUrl":"https://doi.org/10.1109/TIT.2024.3503500","url":null,"abstract":"In this work, we continue the search for quantum locally testable codes (qLTCs) of new parameters by presenting three constructions that can make new qLTCs from old. The first analyses the soundness of a quantum code under Hastings’ weight reduction construction for qLDPC codes to give a weight reduction procedure for qLTCs. Secondly, we describe a novel ‘soundness amplification’ procedure for qLTCs which can increase the soundness of any qLTC to a constant while preserving its distance and dimension, with an impact only felt on its locality. Finally, we apply the AEL distance amplification construction to the case of qLTCs for the first time which can turn a high-distance qLTC into one with linear distance, at the expense of other parameters. These constructions can be used on as-yet undiscovered qLTCs to obtain new parameters, but we also find a number of present applications to prove the existence of codes in previously unknown parameter regimes. In particular, applications of these operations to the hypersphere product code and the hemicubic code yield many previously unknown parameters. In addition, applications of all three results are described to an upcoming work.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"426-458"},"PeriodicalIF":2.2,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10759074","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Tight Lower Bound on the Error Exponent of Classical-Quantum Channels 经典量子信道误差指数的紧下界

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-11-20 DOI: 10.1109/TIT.2024.3500578

Joseph M. Renes

{"title":"Tight Lower Bound on the Error Exponent of Classical-Quantum Channels","authors":"Joseph M. Renes","doi":"10.1109/TIT.2024.3500578","DOIUrl":"https://doi.org/10.1109/TIT.2024.3500578","url":null,"abstract":"A fundamental quantity of interest in Shannon theory, classical or quantum, is the error exponent of a given channel W and rate R: the constant \u0000<inline-formula> <tex-math>$E(W,R)$ </tex-math></inline-formula>\u0000 which governs the exponential decay of decoding error when using ever larger optimal codes of fixed rate R to communicate over ever more (memoryless) instances of a given channel W. Nearly matching lower and upper bounds are well-known for classical channels. Here I show a lower bound on the error exponent of communication over arbitrary classical-quantum (CQ) channels which matches Dalai’s sphere-packing upper bound for rates above a critical value, exactly analogous to the case of classical channels. This proves a conjecture made by Holevo in his investigation of the problem. Unlike the classical case, however, the argument does not proceed via a refined analysis of a suitable decoder, but instead by leveraging a bound by Hayashi on the error exponent of the cryptographic task of privacy amplification. This bound is then related to the coding problem via tight entropic uncertainty relations and Gallager’s method of constructing capacity-achieving parity-check codes for arbitrary channels. Along the way, I find a lower bound on the error exponent of the task of compression of classical information relative to quantum side information that matches the sphere-packing upper bound of Cheng et al. In turn, the polynomial prefactors to the sphere-packing bound found by Cheng et al. may be translated to the privacy amplification problem, sharpening a recent result by Li, Yao, and Hayashi, at least for linear randomness extractors.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"530-538"},"PeriodicalIF":2.2,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Matrix Exponential Generalization of the Laplace Transform of Poisson Shot Noise 泊松散粒噪声拉普拉斯变换的矩阵指数推广

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-11-19 DOI: 10.1109/TIT.2024.3502295

Nicholas R. Olson;Jeffrey G. Andrews

{"title":"A Matrix Exponential Generalization of the Laplace Transform of Poisson Shot Noise","authors":"Nicholas R. Olson;Jeffrey G. Andrews","doi":"10.1109/TIT.2024.3502295","DOIUrl":"https://doi.org/10.1109/TIT.2024.3502295","url":null,"abstract":"We consider a generalization of the Laplace transform of Poisson shot noise defined as an integral transform with respect to a matrix exponential. We denote this as the matrix Laplace transform and establish that it is in general a matrix function extension of the scalar Laplace transform. We show that the matrix Laplace transform of Poisson shot noise admits an expression analogous to that implied by Campbell’s theorem. We demonstrate the utility of this generalization of Campbell’s theorem in two important applications: the characterization of a Poisson shot noise process and the derivation of the complementary CDF (CCDF) and meta-distribution of signal-to-interference-and-noise (SINR) models in Poisson networks. In the former application, we demonstrate how the higher order moments of Poisson shot noise may be obtained directly from the elements of its matrix Laplace transform. We further show how the CCDF of this object may be bounded using a summation of the first row of its matrix Laplace transform. For the latter application, we show how the CCDF of SINR models with phase-type distributed desired signal power may be obtained via an expectation of the matrix Laplace transform of the interference and noise, analogous to the canonical case of SINR models with Rayleigh fading. Additionally, when the power of the desired signal is exponentially distributed, we establish that the meta-distribution may be obtained in terms of the limit of a sequence expressed in terms of the matrix Laplace transform of a related Poisson shot noise process.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"396-412"},"PeriodicalIF":2.2,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A New Algebraic Approach for String Reconstruction From Substring Compositions 一种从子字符串组合重构字符串的新代数方法

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-11-15 DOI: 10.1109/TIT.2024.3493762

Utkarsh Gupta;Hessam Mahdavifar

{"title":"A New Algebraic Approach for String Reconstruction From Substring Compositions","authors":"Utkarsh Gupta;Hessam Mahdavifar","doi":"10.1109/TIT.2024.3493762","DOIUrl":"https://doi.org/10.1109/TIT.2024.3493762","url":null,"abstract":"In this paper, we propose a new algorithm for the problem of string reconstruction from its substring composition multiset. Motivated by applications in polymer-based data storage for recovering strings from tandem mass-spectrometry sequencing, the proposed algorithm leverages the equivalent polynomial formulation of the problem which facilitates efficient parallel implementation. The computational complexity of the proposed reconstruction algorithm is upper bounded by \u0000<inline-formula> <tex-math>$6.5n^{2}$ </tex-math></inline-formula>\u0000 finite field operations, where the field size is upper bounded by \u0000<inline-formula> <tex-math>$10n$ </tex-math></inline-formula>\u0000, implying that the computational complexity is upper bounded by \u0000<inline-formula> <tex-math>$6.5n^{2}(3.22+log {n})$ </tex-math></inline-formula>\u0000 binary operations. Furthermore, it allows parallelization leading to \u0000<inline-formula> <tex-math>$O(n log n)$ </tex-math></inline-formula>\u0000 reconstruction latency. We characterize sufficient conditions for a length n binary string that guarantee the string’s reconstruction time complexity to be bounded polynomially. Moreover, the sufficient conditions on binary strings that guarantee reconstruction in polynomial time are more general than the conditions for the algorithm by Acharya et al. This is used to construct new codebooks of reconstruction codes that have efficient encoding procedures, and are larger, by at least a linear factor in size, compared to the previously best known construction by Pattabiraman et al., (2023).","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"125-137"},"PeriodicalIF":2.2,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Repairing Schemes for Tamo-Barg Codes Tamo-Barg码的修复方案

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-11-14 DOI: 10.1109/TIT.2024.3498033

Han Cai;Ying Miao;Moshe Schwartz;Xiaohu Tang

{"title":"Repairing Schemes for Tamo-Barg Codes","authors":"Han Cai;Ying Miao;Moshe Schwartz;Xiaohu Tang","doi":"10.1109/TIT.2024.3498033","DOIUrl":"https://doi.org/10.1109/TIT.2024.3498033","url":null,"abstract":"In this paper, the repair problem for erasures beyond locality in locally repairable codes is explored under a practical system setting, where a rack-aware storage system consists of racks, each containing a few parity checks. This is referred to as a rack-aware system with locality. Two repair schemes are devised to reduce the repair bandwidth for Tamo-Barg codes under the rack-aware model by setting each repair set as a rack. Additionally, a cut-set bound for locally repairable codes under the rack-aware model with locality is introduced. Using this bound, the second repair scheme is proven to be optimal. Furthermore, the partial-repair problem is considered for locally repairable codes under the rack-aware model with locality, and both repair schemes and bounds are introduced for this scenario.n this paper, the repair problem for erasures beyond locality in locally repairable codes is explored under a practical system setting, where a rack-aware storage system consists of racks, each containing a few parity checks. This is referred to as a rack-aware system with locality. Two repair schemes are devised to reduce the repair bandwidth for Tamo-Barg codes under the rack-aware model by setting each repair set as a rack. Additionally, a cut-set bound for locally repairable codes under the rack-aware model with locality is introduced. Using this bound, the second repair scheme is proven to be optimal. Furthermore, the partial-repair problem is considered for locally repairable codes under the rack-aware model with locality, and both repair schemes and bounds are introduced for this scenario.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"227-243"},"PeriodicalIF":2.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Secure Groupcast: Extra-Entropic Structure and Linear Feasibility 安全组播：超熵结构和线性可行性

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-11-13 DOI: 10.1109/TIT.2024.3497920

Hua Sun

引用次数: 0

Symplectic Self-Orthogonal Quasi-Cyclic Codes 辛自正交拟循环码

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-11-13 DOI: 10.1109/TIT.2024.3497008

Chaofeng Guan;Ruihu Li;Jingjie Lv;Zhi Ma

引用次数: 0

Sparse Regression LDPC Codes 稀疏回归LDPC代码

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-11-12 DOI: 10.1109/TIT.2024.3496486

Jamison R. Ebert;Jean-Francois Chamberland;Krishna R. Narayanan

{"title":"Sparse Regression LDPC Codes","authors":"Jamison R. Ebert;Jean-Francois Chamberland;Krishna R. Narayanan","doi":"10.1109/TIT.2024.3496486","DOIUrl":"https://doi.org/10.1109/TIT.2024.3496486","url":null,"abstract":"This article introduces a novel concatenated coding scheme called sparse regression LDPC (SR-LDPC) codes. An SR-LDPC code consists of an outer non-binary LDPC code and an inner sparse regression code (SPARC), whose respective field size and section sizes are equal. For such codes, an efficient decoding algorithm is proposed based on approximate message passing (AMP) that dynamically shares soft information between inner and outer decoders. This dynamic exchange of information is facilitated by a denoiser that runs belief propagation (BP) on the factor graph of the outer LDPC code within each AMP iteration. It is shown that this BP denoiser falls within the framework of non-separable denoising functions and subsequently, that state evolution holds for the proposed AMP-BP algorithm. Leveraging the rich structure of SR-LDPC codes, this article proposes an efficient low-dimensional approximate state evolution recursion that can be used for efficient hyperparameter tuning, thus paving the way for future work on optimal code design. Finally, numerical simulations demonstrate that SR-LDPC codes outperform contemporary codes over the AWGN channel for parameters of practical interest. SR-LDPC codes are shown to be viable means for obtaining shaping gains over the AWGN channel.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"167-191"},"PeriodicalIF":2.2,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Cover Your Bases: How to Minimize the Sequencing Coverage in DNA Storage Systems 覆盖你的碱基：如何在DNA存储系统中最小化测序覆盖

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-11-12 DOI: 10.1109/TIT.2024.3496587

Daniella Bar-Lev;Omer Sabary;Ryan Gabrys;Eitan Yaakobi

{"title":"Cover Your Bases: How to Minimize the Sequencing Coverage in DNA Storage Systems","authors":"Daniella Bar-Lev;Omer Sabary;Ryan Gabrys;Eitan Yaakobi","doi":"10.1109/TIT.2024.3496587","DOIUrl":"https://doi.org/10.1109/TIT.2024.3496587","url":null,"abstract":"Although the expenses associated with DNA sequencing have been rapidly decreasing, the current cost of sequencing information stands at roughly \u0000<inline-formula> <tex-math>${$}120$ </tex-math></inline-formula>\u0000/GB, which is dramatically more expensive than reading from existing archival storage solutions today. In this work, we aim to reduce not only the cost but also the latency of DNA storage by initiating the study of the DNA coverage depth problem, which aims to reduce the required number of reads to retrieve information from the storage system. Under this framework, our main goal is to understand the effect of error-correcting codes and retrieval algorithms on the required sequencing coverage depth. We establish that the expected number of reads that are required for information retrieval is minimized when the channel follows a uniform distribution. We also derive upper and lower bounds on the probability distribution of this number of required reads and provide a comprehensive upper and lower bound on its expected value. We further prove that for a noiseless channel and uniform distribution, MDS codes are optimal in terms of minimizing the expected number of reads. Additionally, we study the DNA coverage depth problem under the random-access setup, in which the user aims to retrieve just a specific information unit from the entire DNA storage system. We prove that the expected retrieval time is at least k for \u0000<inline-formula> <tex-math>$[n,k]$ </tex-math></inline-formula>\u0000 MDS codes as well as for other families of codes. Furthermore, we present explicit code constructions that achieve expected retrieval times below k and evaluate their performance through analytical methods and simulations. Lastly, we provide lower bounds on the maximum expected retrieval time. Our findings offer valuable insights for reducing the cost and latency of DNA storage.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"192-218"},"PeriodicalIF":2.2,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0